PHY101🔧🔩. PROJECTILE

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*PROJECTILE🏹🏓*

```Definition of a Projectile```

A *Projectile* may be defined as a body or an object that's been propelled(projected) by the application of an external force in which the object then moves freely under the action/influence of gravity

Let us take a look at the concept of projectile in this manner as when a boy releases a piece of stone from his catapult against a bird perching on a tree branch, the stone travels in a parabolic path towards the bird

That's an example of a projectile motion

A *Trajectory* is a Parabolic path with which a projectile moves or travels

*Examples of Projectile Motion are:*

🔫A bullet from a fired gun
🏹A Stone or arrow released from a catapult
🤸🏻‍♂️An Athlete doing the high jump
🤾‍♀️A thrown rubber ball rebouncing from a wall
🏓A tennis ball thrown against a wall
⚽When we throw a ball from the top of a building
>A stone released from a catapult against a bird on a tree

Let's take a look at this expression below:

Let us first consider a simple case of a stone thrown horizontally with an initial velocity, U from the top of a high wall or a cliff of height, h. The Stone is subject to two independent motions;

_A Horizontal_ and _A Vertical_. Once the stone is free and before it hits the ground, no horizontal force acts upon it. Therefore, it's horizontal velocity will remain unchanged until it hits the ground.

When the stone is initially thrown forward, It has no vertical velocity. But the vertical pull of gravity would accelerate it downwards at a rate of about 9.8m/s². The vertical y-component of the velocity will then increase by 9.8m/s every second.

Hence, any projectile in flight is doing two things at once:
1. It is flying horizontally with a constant speed.
2. It is moving up or down with an acceleration, g.

*TERMS IN PROJECTILE*

⏰Time taken(to reach the maximum height), t : This is the time required for a projectile to travel from its point of projection to its maximum height, H. It's mathematically expressed as t = usin∅/g where U = initially velocity and g = acceleration due to gravity. (Note, g = 9.8m/s²)

🕰️Time of Flight, T : This is the time required for a projectile to return to the same level from which it was projected. it's also the Total time taken. It Is mathematically expressed as T = 2usin∅/g

🛝Maximum Height, H:  This is the Highest vertical distance attained as measured from the horizontal projection plane of reference. It's mathematically expressed as: H = (U²sin²∅)/2g

⛳Range,R:: This is the horizontal distance from the point of projection to the point where the projectile hits the projection plane again. It's mathematically expressed as R = (U²sin2∅)/g

*NOTE THAT*: The range is maximum when sin 2∅ of the equation [R=(U²sin2∅)/g] is maximum. The sine of an angle is maximum when the angle Is 90°. Thus, the maximum value of sin2∅ equals 1 when 2∅ equals 90° or better still,, when ∅ = 45°.
So, R = R(max) at ∅ = 45°
It could be mathematically expressed as: R(max) = U²/g.

Thus, the maximum horizontal range is attained when the projection angle is *45°*

KINDLY TREAT SOME QUESTIONS ON PROJECTILE

*Written by:*
     Mr. Adebayo Ayomide

✍️ *FLASHPEE EDUCATIONAL TEAM*

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